If f x is a non-negative function such that the area bounded by y = f x , x -axis and the lines x = 0 and x = α is 4 α sin ⁡ α + 2 sq. units ∀ α ∈ 0 , π , then the value of f π 2 is equal to

Step-by-step solution

Given, ∫ 0 α f x d x = 4 α sin ⁡ α + 2 On differentiating with respect to α , we get, f α = 4 α ⋅ cos α + 4 sin α ∴ f π 2 = 4